/*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee.  All rights reserved.

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
      pseudocode.

See subroutines comments for additional copyrights.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

- Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer listed
  in this license in the documentation and/or other materials
  provided with the distribution.

- Neither the name of the copyright holders nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/

#ifndef _srcond_h
#define _srcond_h

#include "ap.h"
#include "ialglib.h"

#include "ldlt.h"
#include "ssolve.h"
#include "estnorm.h"


/*************************************************************************
Condition number estimate of a symmetric matrix

The algorithm calculates a lower bound of the condition number. In this
case, the algorithm does not return a lower bound of the condition number,
but an inverse number (to avoid an overflow in case of a singular matrix).

It should be noted that 1-norm and inf-norm condition numbers of symmetric
matrices are equal, so the algorithm doesn't take into account the
differences between these types of norms.

Input parameters:
    A       -   symmetric definite matrix which is given by its upper or
                lower triangle depending on IsUpper.
                Array with elements [0..N-1, 0..N-1].
    N       -   size of matrix A.
    IsUpper -   storage format.

Result:
    1/LowerBound(cond(A))
*************************************************************************/
double smatrixrcond(const ap::real_2d_array& a, int n, bool isupper);


/*************************************************************************
Condition number estimate of a matrix given by LDLT-decomposition

The algorithm calculates a lower bound of the condition number. In this
case, the algorithm does not return a lower bound of the condition number,
but an inverse number (to avoid an overflow in case of a singular matrix).

It should be noted that 1-norm and inf-norm condition numbers of symmetric
matrices are equal, so the algorithm doesn't take into account the
differences between these types of norms.

Input parameters:
    L       -   LDLT-decomposition of matrix A given by the upper or lower
                triangle depending on IsUpper.
                Output of SMatrixLDLT subroutine.
    Pivots  -   table of permutations which were made during LDLT-decomposition,
                Output of SMatrixLDLT subroutine.
    N       -   size of matrix A.
    IsUpper -   storage format.

Result:
    1/LowerBound(cond(A))
*************************************************************************/
double smatrixldltrcond(const ap::real_2d_array& l,
     const ap::integer_1d_array& pivots,
     int n,
     bool isupper);


/*************************************************************************
Obsolete 1-based subroutine
*************************************************************************/
double rcondsymmetric(ap::real_2d_array a, int n, bool isupper);


/*************************************************************************
Obsolete 1-based subroutine
*************************************************************************/
double rcondldlt(const ap::real_2d_array& l,
     const ap::integer_1d_array& pivots,
     int n,
     bool isupper);


void internalldltrcond(const ap::real_2d_array& l,
     const ap::integer_1d_array& pivots,
     int n,
     bool isupper,
     bool isnormprovided,
     double anorm,
     double& rcond);


#endif
